Simplify (-45-22i)+2(5-3i)(5+3i)

$(- 45 - 22 i) + 2 (5 - 3 i) (5 + 3 i)$

Simplify each term.

Apply the distributive property.

$- 45 - 22 i + (2 \cdot 5 + 2 (- 3 i)) (5 + 3 i)$

Multiply $2$ by $5$ .

$- 45 - 22 i + (10 + 2 (- 3 i)) (5 + 3 i)$

Multiply $- 3$ by $2$ .

$- 45 - 22 i + (10 - 6 i) (5 + 3 i)$

Expand $(10 - 6 i) (5 + 3 i)$ using the FOIL Method.

Apply the distributive property.

$- 45 - 22 i + 10 (5 + 3 i) - 6 i (5 + 3 i)$

Apply the distributive property.

$- 45 - 22 i + 10 \cdot 5 + 10 (3 i) - 6 i (5 + 3 i)$

Apply the distributive property.

$- 45 - 22 i + 10 \cdot 5 + 10 (3 i) - 6 i \cdot 5 - 6 i (3 i)$

Simplify and combine like terms.

Simplify each term.

Multiply $10$ by $5$ .

$- 45 - 22 i + 50 + 10 (3 i) - 6 i \cdot 5 - 6 i (3 i)$

Multiply $3$ by $10$ .

$- 45 - 22 i + 50 + 30 i - 6 i \cdot 5 - 6 i (3 i)$

Multiply $5$ by $- 6$ .

$- 45 - 22 i + 50 + 30 i - 30 i - 6 i (3 i)$

Multiply $- 6 i (3 i)$ .

Multiply $3$ by $- 6$ .

$- 45 - 22 i + 50 + 30 i - 30 i - 18 i i$

Raise $i$ to the power of $1$ .

$- 45 - 22 i + 50 + 30 i - 30 i - 18 (i^{1} i)$

Raise $i$ to the power of $1$ .

$- 45 - 22 i + 50 + 30 i - 30 i - 18 (i^{1} i^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 45 - 22 i + 50 + 30 i - 30 i - 18 i^{1 + 1}$

Add $1$ and $1$ .

$- 45 - 22 i + 50 + 30 i - 30 i - 18 i^{2}$

Rewrite $i^{2}$ as $- 1$ .

$- 45 - 22 i + 50 + 30 i - 30 i - 18 \cdot - 1$

Multiply $- 18$ by $- 1$ .

$- 45 - 22 i + 50 + 30 i - 30 i + 18$

Add $50$ and $18$ .

$- 45 - 22 i + 68 + 30 i - 30 i$

Subtract $30 i$ from $30 i$ .

$- 45 - 22 i + 68 + 0$

Add $68$ and $0$ .

$- 45 - 22 i + 68$

Add $- 45$ and $68$ .

$23 - 22 i$

Simplify (-45-22i)+2(5-3i)(5+3i)

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